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The QCD axion, which may solve the Strong CP problem, and axion-like particles, which arise naturally in many models of high-scale physics, provide theoretically compelling dark-matter and dark-sector candidates. The extreme environments characterized by large magnetic fields, high densities, and high temperatures realized in astrophysical contexts provide natural laboratories to search for axions which couple to electromagnetism and matter. In this talk, I will discuss recent results and ongoing work towards the discovery of axions using radio and X-ray observations of neutron stars and super star clusters. In particular, I will focus on dedicated radio searches using the Effelsberg and Greenbank Telescopes that have resulted in new constraints on axion DM in the 1-10 mueV range. I will also discuss recent analyses of archival X-Ray data from the XMM-Newton, Chandra, and NuSTAR telescopes with implications for ultralight axions.